Freeness conjecture for pattern Hopf algebras of associative presheaves

Let $h$ be an associative presheaf, and let $\mathcal{A}(h)$ denote its pattern Hopf algebra. Freeness conjecture. The pattern Hopf algebra $\mathcal{A}(h)$ is free. This would establish freeness uniformly for pattern Hopf algebras arising from associative presheaves; the supplied text gives the general strategy for proving such results but does not state whether this claim has been resolved.